Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1e2;
int n, m;
int g[MAXN][MAXN];
int addn[MAXN], addm[MAXN];
int go(int beg) {
  addn[0] = beg;
  for (int i = 1; i < n; i++) addn[i] = addn[i - 1] + g[i][0] - g[i - 1][0];
  addm[0] = g[0][0] - beg;
  for (int j = 1; j < m; j++) addm[j] = addm[j - 1] + g[0][j] - g[0][j - 1];
  for (int i = 0; i < n; i++)
    if (addn[i] < 0) return 1e9;
  for (int j = 0; j < m; j++)
    if (addm[j] < 0) return 1e9;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++)
      if (addn[i] + addm[j] != g[i][j]) return 1e9;
  int res = 0;
  for (int i = 0; i < n; i++) res += addn[i];
  for (int j = 0; j < m; j++) res += addm[j];
  return res;
}
int32_t main() {
  cin >> n >> m;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) cin >> g[i][j];
  for (int i = 0; i < n - 1; i++)
    for (int j = 0; j < m; j++)
      if (g[i + 1][j] - g[i][j] != g[i + 1][0] - g[i][0]) {
        cout << -1 << endl;
        return 0;
      }
  for (int j = 0; j < m - 1; j++)
    for (int i = 0; i < n; i++)
      if (g[i][j + 1] - g[i][j] != g[0][j + 1] - g[0][j]) {
        cout << -1 << endl;
        return 0;
      }
  int ans = 1e9, b = -1;
  for (int beg = 0; beg <= g[0][0]; beg++) {
    int cur = go(beg);
    if (cur < ans) ans = cur, b = beg;
  }
  go(b);
  cout << ans << endl;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < addn[i]; j++) cout << "row " << i + 1 << endl;
  for (int j = 0; j < m; j++)
    for (int i = 0; i < addm[j]; i++) cout << "col " << j + 1 << endl;
  return 0;
}